Error Modeling and Simulation of Serial-Parallel Mechanism Based on Screw Theory

Abstract:

Focus on the problems of calculation complexity and abstractness in the traditional analysis methods of serial-parallel mechanism, the complete kinematic product of exponentials formula of serial-parallel mechanism was established in the paper based on the screw representation of spatial rigid motion. The errors of 4 D-H parameters were equivalent to error screw and the practical screw coordinate containing error screw of every joint axis was established. After the practical kinematic product of exponentials formula of serial-parallel mechanism being derived, the pose error model of tool coordinate system was established. According to the above screw method, numerical calculation of cutting machine about kinematic and error analysis was performed with MATLAB and the calculation results were compared with the simulation results of ADAMS. The comparison results show that relative error of the two groups of calculation results is within the 0.001 orders of magnitude and the correctness of screw methods application in the analysis of serial-parallel mechanism.

• Periodical: Applied Mechanics and Materials (Volume 527)
• Pages: 156-161
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.527.156
• Online since: February 2014
• Authors: Sheng Hai Hu, Xiu Lian Liu*, Jun Chao Sun, Ting Ting Xie, Song Qi
• Keywords: Error Modeling, Error Screw, Product of Exponentials Formula, Screw Theory

References

[1] Richard Morel, Zexiang Li, Shane Terry, sass card. A mathematical introduction of robotic operation[M]. Bejing: Machinery Industry Press，(1998).

[2] MURRAY R W, LI Z, SASTRY S S. A mathematical introduction to robot manipulation[M]. Boca Raton: CRC Press, (1993).

[3] Veitschegger W K, Wu Chi-haur. Method for calibration and compensation robot kinematic errors[C]. Proceedings of the 1987 International Conference on Robotics and Automation. New York: IEEE, (1987).

DOI: 10.1109/robot.1987.1087839

[4] Stone H W, Sanderson A C. A prototype arm signature identification system[C]. Proceedings of the 1987 International Conference on Robotics and Automation. New York: IEEE, 1987.

DOI: 10.1109/robot.1987.1087835

[5] Liming Xin, Zhigang Xu, Mingyang Zhao. Chinese Journal of Mechanical Engineering, China 2010. 42(2): P62-68.

[6] MOON S K, MOON Y M. Screw Theory Based Metrology for Design and Error Compensation of Machine Tools[C] /Proceedings of the ASME Design Engineering Technical Conference. America, September 9, 2001: V2, 697-707.

DOI: 10.1115/detc2001/dac-21083

[7] MOON S K. Error prediction and compensation of reconfigurable machine tool using screw kinematics[D]. U S A: The University of Mchigan, (2002).

[8] Li Du, Yonggang Huang, Cangpin Zhou. The Chinese society of Agricultural Engineering, 2010, 26(6): P157-162.

[9] Zhen Huang, Yongsheng Zhao, Tieshi Zhao. Higher spatial mechanism[M]. Bejing: Higher Education Press，(2006).